Polyester-based fiber materials that are polyester fiber materials and composites thereof with other fiber materials are usually dyed under high temperature conditions of 100-140° C., but polyester oligomers cause various troubles by eluting from the polyester-based fiber material onto the fiber surfaces or into the dyeing bath. The serious problems that are faced are shadow spots or calender contamination that occur when the polyester-based fiber material is a fabric, and powder generation or winding yarn breakage that occur when it is a yarn. In order to solve such problems, methods have been adopted that involve adding oligomer removing agents to the dyeing bath or to the reduction/cleaning bath after dyeing. For example, Japanese Unexamined Patent Publication No. 2000-154466 discloses a method for preventing trouble resulting from oligomer deposition, by adding to the dyeing bath an oligomer removing agent comprising a sulfonic acid salt of polyoxyethylenestyryl phenyl ether, and a carboxyl group-containing polymer such as an acrylic acid or methacrylic acid polymer or a salt thereof. Also, Japanese Unexamined Patent Publication No. 2001-295136 discloses a method for preventing oligomer elution wherein during the dyeing step there is added to the dyeing bath an oligomer preventing agent comprising an ester of a polyhydric alcohol-alkylene oxide addition product and an alkyl or alkenyl fatty acid, or an ester obtained by transesterification between a polyhydric alcohol-alkylene oxide addition product and a natural animal or vegetable fat or oil containing an alkyl or alkenyl fatty acid. However, the polyester oligomer removing effect is low even with addition of such oligomer removing agents or preventing agents, and it is not possible at the current time to achieve a satisfactory oligomer removing effect, especially with acidic baths.